Surfaces generated by moving least squares methods

Authors:
P. Lancaster and K. Salkauskas

Journal:
Math. Comp. **37** (1981), 141-158

MSC:
Primary 65D05; Secondary 41A05, 41A63

MathSciNet review:
616367

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Abstract: An analysis of moving least squares (m.l.s.) methods for smoothing and interpolating scattered data is presented. In particular, theorems are proved concerning the smoothness of interpolants and the description of m.l.s. processes as projection methods. Some properties of compositions of the m.l.s. projector, with projectors associated with finiteelement schemes, are also considered. The analysis is accompanied by examples of univariate and bivariate problems.

**[1]**Robert E. Barnhill,*Representation and approximation of surfaces*, Mathematical software, III (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1977) Academic Press, New York, 1977, pp. 69–120. Publ. Math. Res. Center Univ. Wisconsin, No. 39. MR**0489081****[2]**R. W. Clough & J. L. Tocher, "Finite element stiffness matrices for analysis of plates in bending," in*Proc. Conf. Matrix Methods in Structural Mechanics*, Wright-Patterson A.F.B., Ohio, 1965.**[3]**Richard Franke and Greg Nielson,*Smooth interpolation of large sets of scattered data*, Internat. J. Numer. Methods Engrg.**15**(1980), no. 11, 1691–1704. MR**593596**, 10.1002/nme.1620151110**[4]**William J. Gordon and James A. Wixom,*Shepard’s method of “metric interpolation” to bivariate and multivariate interpolation*, Math. Comp.**32**(1978), no. 141, 253–264. MR**0458027**, 10.1090/S0025-5718-1978-0458027-6**[5]**Peter Lancaster,*Moving weighted least-squares methods*, Polynomial and spline approximation (Proc. NATO Adv. Study Inst., Univ. Calgary, Calgary, Alta., 1978) NATO Adv. Study Inst. Ser., Ser. C: Math. Phys. Sci., vol. 49, Reidel, Dordrecht-Boston, Mass., 1979, pp. 103–120. MR**545641****[6]**Peter Lancaster,*Composite methods for generating surfaces*, Polynomial and spline approximation (Proc. NATO Adv. Study Inst., Univ. Calgary, Calgary, Alta., 1978) NATO Adv. Study Inst. Ser., Ser. C: Math. Phys. Sci., vol. 49, Reidel, Dordrecht-Boston, Mass., 1979, pp. 91–102. MR**545640****[7]**D. H. Mclain, "Drawing contours from arbitrary data points,"*Comput. J.*, v. 17, 1974, pp. 318-324.**[8]**Lois Mansfield,*Higher order compatible triangular finite elements*, Numer. Math.**22**(1974), 89–97. MR**0351040****[9]**M. J. D. Powell and M. A. Sabin,*Piecewise quadratic approximations on triangles*, ACM Trans. Math. Software**3**(1977), no. 4, 316–325. MR**0483304****[10]**S. Ritchie,*Representation of Surfaces by Finite Elements*, M.Sc. Thesis, University of Calgary, 1978.**[11]**D. Shepard,*A Two-Dimensional Interpolation Function for Irregularly Spaced Points*, Proc. 1968 A.C.M. Nat. Conf., pp. 517-524.

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DOI:
http://dx.doi.org/10.1090/S0025-5718-1981-0616367-1

Article copyright:
© Copyright 1981
American Mathematical Society